Tilt error corrective scanning optical system

ABSTRACT

A tilt error corrective scanning optical system for use in a laser scanning machine such as a laser printer. The system comprises a linear image forming optical device for causing a beam to form a linear image on a deflecting device, and a scanning image forming optical device for causing the beam deflected by the deflecting device to form an image on a scanned object. The scanning image forming optical device includes a first lens disposed between the deflecting element and the scanned object, and a second lens disposed at a side of the first lens opposed to the scanned object. The second lens includes a toric surface opposed to the scanned object. A surface of the second lens opposed to the deflecting element, a surface of the first lens opposed to the scanned object or a surface of the first lens opposed to the deflecting element defines a cylindrical surface having a refracting power in a direction perpendicular to a scanning plane.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

The present invention relates to a tilt error corrective scanningoptical system mainly used in a laser printer or the like foreliminating scanning pitch slippage of scanning lines in an auxiliaryscanning direction.

More particularly, the present invention relates to a tilt errorcorrective scanning optical system comprising a linear image formingoptical device for causing a beam emitted from a light source to form alinear image on a deflecting and reflecting surface of deflecting means,and a scanning image forming optical device for causing the beamreflected and deflected by the deflecting means to form an image on ascanned object.

(2) Description of the Prior Art

In recent years, there is an increasing demand for the laser beamprinter in accordance with diversification and development of officeautomating machines because of becoming smaller and cheaper as well asadvantage of high speed printing. With the laser beam printer includingdeflecting means such as a polygonal mirror for deflecting a beamemitted from a light source, for example, there occur tilt errors withrespect to a direction perpendicular to a scanning plane (in the case ofa polygonal mirror, tilt errors with respect to an axis of revolution ofreflecting surfaces) which are caused by manufacturing errors, assemblyerrors or vibrations at times of rotation of the mirror.

The beam reflected by a deflecting and reflecting surface having sucherrors results in an image forming position on a scanned object slippedor deviated in an auxiliary scanning direction and a nonuniformity inthe scanning line pitch. In the case of a recording apparatus such asthe laser beam printer, for example, the nonuniformity in the scanningline pitch deteriorates the quality of recorded images.

The aforesaid tilt error corrective scanning optical systems is designedfor eliminating the nonuniformity in the scanning line pitch. The beamemitted from the light source is once converged by the linear imageforming optical device in a direction perpendicular to the scanningplane to form a linear image on a deflecting and reflecting surface ofthe deflecting means. The beam from a point of deflection and reflectionis restored in the above direction by the scanning image forming opticalsystem to form a conjugate image on the scanned object. This processsubstantially precludes the influence of the tilt errors of thedeflecting and reflecting surface.

On the other hand, the tilt error corrective optical system causes thebeam to form on the scanned object an image having a height proportionalto an incident angle of the beam on the scanning image forming opticaldevice, so that the beam scans the object at a constant scanning speed.

In this specification the term "scanning plane" means a plane formed bya time series set of the scanning beam, namely a plane including mainscanning lines on the scanned object and an optical axis of the tiltcorrective scanning optical system.

Various construction of the tilt corrective scanning optical system havebeen proposed heretofore.

One example is disclosed in U.S. Pat. No. 3,750,189. This constructioncomprises a scanning image forming optical device including a beamshaping optical element such as a cylindrical lens for restoring thebeam into a circular form, which beam has been converged into a line bya linear image forming optical element and reflected by deflectingmeans, and a converging optical element for converging the restored beamto form an image on the scanned object.

Where the beam is restored by the beam shaping optical element as in theabove construction, the restrictive condition to regain the circularbeam is imposed on the beam shaping optical element. As a result, thereis a reduced freedom for improving distortion characteristics providedfor the converging optical element to realize the constant scanningspeed of the beam and image forming characteristics for forming imageson the scanned object. In order to realize excellent distortion andimage forming characteristics, the scanning image forming optical devicerequires many lenses, thereby complicating the optical deviceconstruction.

The Japanese patent application laid open under No. 50-93720 discloses aproposal for improving the foregoing prior construction. In thisconstruction, a beam shaping optical element such as a cylindrical lensas noted above is interposed between the converging optical element andthe scanned object.

With this construction, the beam shaping optical element must be locatedclose to the scanned object in order to produce high quality images. Itis therefore necessary for the beam shaping optical element to be longin the main scanning direction, which is contrary to a compactconstruction.

A further known construction is disclosed in U.S. Pat. No. 4,379,612wherein the scanning image forming optical device disposed between thedeflecting means and the scanned object comprises a single sphericallens and a single lens including a toric surface, the latter beingdisposed at a side of the single spherical lens opposed to the scannedobject. This scanning image forming optical device has the distortioncharacteristics for realizing the constant speed scanning of the beam aswell as the function to correct the tilt errors of the deflecting andreflecting surfaces in cooperation with the linear image forming opticalsystem.

Although this construction realizes a compact optical system, only alimited freedom is provided thereby. For example, it is difficult toenlarge the field angle for increasing the scanning range of the beamwhere both the distortion characteristics for realizing the constantspeed scanning of the beam and the function to correct the tilt errorsof the deflecting and reflecting surfaces are maintained in an excellentstate.

SUMMARY OF THE INVENTION

The object of the present invention is to eliminate the disadvantages ofthe known optical systems and to provide a compact tilt error correctiveoptical system comprising a linear image forming optical device forcausing a beam emitted from a light source to form a linear image on adeflecting and reflecting surface of deflecting means and a scanningimage forming optical device for causing the beam reflected anddeflected by the deflecting means to form an image on a scanned object,this optical system permitting the field angle to be enlarged in themain scanning direction while maintaining excellent image formingcharacteristics and an excellent tilt error correcting function.

The foregoing object is accomplished in one preferred embodiment of theinvention by providing a scanning image forming optical device forcausing the beam reflected and deflected by the deflecting means to forman image on a scanned object, the scanning image forming optical deviceconsisting of a first lens disposed between the deflecting means and thescanned object, and a second lens disposed at a side of the first lensopposed to the scanned object, wherein the first lens includes acylindrical surface, and the second lens defines a toric surface.

The term "toric surface" hereinafter used refers to a refracting surfacehaving one refracting power in the main scanning direction of the beamand another refracting power in the auxiliary scanning direction whichis perpendicular to the main scanning direction, in a planeperpendicular to the optical axis of the tilt corrective scanningoptical system.

The term "cylindrical surface" refers to one form of toric surfacehaving a refracting power only in either the main scanning direction orthe auxiliary scanning direction.

In the construction defined above, the cylindrical surface and toricsurface are provided by different lenses. This feature enables the tiltcorrective scanning optical system to maintain excellent image formingcharacteristics over a very wide range in the direction perpendicular tothe scanning plane, thereby increasing the designing freedom. Thisdiminishes designing restrictions in the direction parallel to thescanning plane. In this direction the optical system is capable ofmaintaining excellent image forming characteristics and enlarging thefield angle while having distortion characteristics for maintainingsufficiently reliable constant speed scanning of the scanned object bythe beam.

Furthermore, this optical system has a wide range of magnification whilemaintaining a deflecting and reflecting point on the deflecting meansand an image forming point on the scanned object in conjugation withrespect to the scanning image forming optical device in the directionperpendicular to the scanning plane. The lower the magnification, thebetter is the effect of tilt error correction. Conversely, the higherthe magnification, the better the image forming characteristics tend tobecome. Thus, magnification may be set in accordance with requiredperformance.

The increased designing freedom as described above allows a small sizeoptical system to be designed with ease to fulfill desired performance.Thus the optical system may be able to provide a large field angle andhave a compact construction.

According to a further development of this embodiment, the first andsecond lenses include plane and spherical surfaces opposed to thecylindrical and toric surfaces, respectively. This feature provides foraccurate position setting at times of shaping the cylindrical and toricsurfaces, thereby to facilitate shaping work.

In particular, the cylindrical surface of the first lens has a negativerefracting power in the direction perpendicular to the scanning plane,and the first lens as a whole has a negative refracting power in thisdirection. This construction promotes the image forming characteristicsover a wide range in this direction.

The negative cylindrical surface may be defined at a side of the firstlens opposed to the deflecting means. This realizes an optical systemproviding a wide field angle and capable of effectively correcting tilterrors of the deflecting and reflecting surfaces of the deflecting meanswhich is carried out through this negative cylindrical surface and thetoric surface of the second lens.

It is advantageous if the second lens has a concave surface opposed tothe deflecting means. This enables the optical system to have good imageforming characteristics in the direction perpendicular to the scanningplane while promoting the constant speed scanning of the beam with adistortion provided in the direction parallel to the scanning plane.

In a still further development of this embodiment, the negativecylindrical surface is defined on the side of the first lens opposed tothe scanned object. This enables the optical system to have excellentimage forming characteristics over a wide range of the scanned object inthe direction perpendicular to the scanning plane.

It is still further advantageous if the following conditions (A) and (B)are satisfied to maintained excellent image forming characteristics:

    f1H<0                                                      (A)

wherein f1H is a focal length of the first lens in the directionparallel to the scanning plane, and

    |f1H/f1V|>2                              (B)

wherein f1V is a focal length of the first lens in the directionperpendicular to the scanning plane.

The condition (A) relates mainly to the distortion deliberately providedin the direction parallel to the scanning plane in order to realize theconstant speed scanning of the beam on the scanned object. Where thiscondition is not satisfied, it is difficult to maintain reliableconstant speed scanning over a wide field angle, which renders theoptical system unfit for practical use.

The condition (B) is mainly for correcting spherical aberration andfield curvature in the direction perpendicular to the scanning plane.Where this condition is not satisfied, it is difficult to correct theabove two aberrations with a good balance over a wide field angle.Particularly where the field curvature is not sufficiently corrected,the spot size varies on the scanning lines which deteriorates imagequality.

The object of the present invention is accomplished in anotherembodiment by providing a scanning image forming optical device forcausing the beam reflected and deflected by the deflecting means to forman image on a scanned object, the scanning image forming optical deviceconsisting of a first lens disposed between the deflecting means and thescanned object, and a second lens disposed at a side of the first lensopposed to the scanned object, wherein the first lens comprises acylindrical lens having no refracting power in a direction parallel to ascanning plane, and the second lens includes a toric surface.

This construction produces effects similar to those of the foregoingembodiment. As in the foregoing embodiment, the two lenses constitutingthe scanning image forming optical device include a plane surfaceopposed to the cylindrical surface and a spherical surface opposed tothe toric surface, respectively. This feature provides for accurateposition setting at times of shaping the cylindrical and toric surfaces,thereby to facilitate shaping work.

The cylindrical surface is defined at a side of the cylindrical lensopposed to the scanned object and has a negative refracting power in thedirection perpendicular to the scanning plane. This realizes an opticalsystem providing a wide field angle and capable of correcting tilterrors of the deflecting and reflecting surfaces of the deflecting meanswith enhanced reliability which is carried out through this negativecylindrical surface and the toric surface of the second lens.

The second lens may include a concave surface opposed to the deflectingmeans to provide the same advantage as noted hereinbefore.

The object of the present invention may be accomplished in a furtherembodiment by providing a scanning image forming optical device forcausing the beam reflected and deflected by the deflecting means to forman image on a scanned object, the scanning image forming optical deviceconsisting of a first lens disposed between the deflecting means and theobject scanned, and a second lens disposed at a side of the first lensopposed to the scanned object, wherein the first lens includes a firstcylindrical surface having an axis extending perpendicular to a scanningplane and a second cylindrical surface having an axis extendingperpendicular to an optical axis in the scanning plane, and the secondlens includes a toric surface.

This construction also produces effects similar to those of theforegoing embodiments. The aspect of this embodiment worthy of specialmention is that the cylindrical surface having an axis extendingperpendicular to the scanning plane increases the designing freedom inthe direction parallel to the scanning plane, thereby to secureexcellent constant speed scanning over a wide field angle.

In this embodiment the second lens includes a plane or spherical surfaceopposed to the toric surface. This feature provides for accurateposition setting at times of shaping the toric surface, thereby tofacilitate shaping work as in the case of the foregoing embodiments.

The second cylindrical surface of the first lens having an axisextending perpendicular to the optical axis in the scanning plane isopposed to the deflecting means and has a negative refracting power.This realizes an optical system providing a wide field angle and capableof effectively correcting tilt errors of the deflecting and reflectingsurfaces of the deflecting means with which is carried out through thisnegative cylindrical surface and the toric surface of the second lens.

Further, the second lens may include a concave surface opposed to thedeflecting means to provide the same advantage as noted hereinbefore.

With this embodiment also, excellent image forming characteristics maybe maintained by satisfying the conditions (A) and (B) set outhereinbefore.

The object of the present invention may be accomplished in a stillfurther embodiment by providing a scanning image forming optical devicefor causing the beam reflected and deflected by the deflecting means toform an image on a scanned object, the scanning image forming opticaldevice consisting of a first lens disposed between the deflecting meansand the scanned object, and a second lens disposed at a side of thefirst lens opposed to the scanned object, wherein the first lensincludes a cylindrical surface having an axis extending perpendicular toa scanning plane, and the second lens includes a cylindrical surfacehaving an axis extending perpendicular to a scanning plane, and thesecond lens includes a cylindrical surface having an axis extendingperpendicular to an optical axis in the scanning plane, and a toricsurface.

This construction also produces effects similar to those of theforegoing embodiments. The aspect of this embodiment worthy of specialmention is that the first lens includes a cylindrical surface having anaxis extending perpendicular to the scanning plane and this increasesthe designing freedom in the direction parallel to the scanning plane.In this direction the optical system is capable of maintaining excellentimage forming characteristics and enlarging the field angle while havingdistortion characteristics for maintaining sufficiently reliableconstant speed scanning of the scanned object by the beam.

This feature allows the optical system to maintain excellent imageforming characteristics over a wide range in the direction perpendicularto the scanning plane which is achieved through the cylindrical surfaceand toric surface of the second lens.

With this embodiment too, it is advantageous if the cylindrical surfaceof the second lens is defined on the side opposed to the deflectingmeans to have a negative refracting power in the direction perpendicularto the scanning plane. The cylindrical surface having a negativerefracting power in the direction perpendicular to the scanning planeenables the optical system to have sufficient image formingcharacteristics over a wide range in that direction.

With this embodiment, excellent image forming characteristics may bemaintained by satisfying the condition (A) set out hereinbefore.

The four embodiments for accomplishing the object of the presentinvention have been described along with several modifications thereof.The common basic concept of the various constructions according to theinvention resides in a scanning image forming optical device for causingthe beam reflected and deflected by the deflecting means to form animage on a scanned object, the scanning image forming optical deviceconsisting of a first lens disposed between the deflecting means and thescanned object, and a second lens disposed at a side of the first lensopposed to the scanned object, wherein the second lens includes a toricsurface opposed to the scanned object, and one of a surface of thesecond lens opposed to the deflecting means, a surface of the first lensopposed to the scanned object and a surface of the first lens opposed tothe deflecting means defines a cylindrical surface having a refractingpower in a direction perpendicular to a scanning plane.

Other object, features and advantages of the present invention will beapparent from the following description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B through FIGS. 5A and 5B show various examples of lensarrangement in a scanning image forming optical device of a tilt errorcorrective scanning optical system according to a first embodiment ofthe present invention, in which FIGS. 1A through 5A are sectional viewstaken in a direction parallel to a scanning plane, and FIGS. 1B through5B are sectional views taken in a direction perpendicular to thescanning plane.

FIGS. 6 through 10 are aberration diagrams in the direction parallel tothe scanning plane in the examples of lens arrangement according to thefirst embodiment.

FIGS. 11 through 15 are aberration diagrams in the direction parallel tothe scanning plane in the examples of lens arrangement according to thefirst embodiment.

FIGS. 16A, 16B, 17A and 17B show examples of lens arrangement in ascanning image forming optical device of a tilt error correctivescanning optical system according to a second embodiment of the presentinvention, in which FIGS. 16A and 17A are sectional views taken in thedirection parallel to the scanning plane, and FIGS. 16B and 17B aresectional views taken in the direction perpendicular to the scanningplane.

FIGS. 18 and 19 are aberration diagrams in the direction parallel to thescanning plane in the examples of lens arrangement according to thesecond embodiment.

FIGS. 20 and 21 are aberration diagrams in the direction perpendicularto the scanning plane in the examples of lens arrangement according tothe second embodiment.

FIGS. 22A and 22B through FIGS. 24A and 24B show examples of lensarrangement in a scanning image forming optical device of a tilt errorcorrective scanning optical system according to a third embodiment ofthe present invention, in which FIGS. 22A through 24A are sectionalviews taken in the direction parallel to the scanning plane, and FIGS.22B through 24B are sectional views taken in the direction perpendicularto the scanning plane.

FIGS. 25 through 27 are aberration diagrams in the direction parallel tothe scanning plane in the examples of lens arrangement according to thethird embodiment.

FIGS. 28 through 30 are aberration diagrams in the directionperpendicular to the scanning plane in the examples of lens arrangementaccording to the third embodiment.

FIGS. 31A and 31B through FIGS. 33A and 33B show examples of lensarrangement in a scanning image forming optical device of a tilt errorcorrective scanning optical system according to a fourth embodiment ofthe present invention, in which FIGS. 31A through 33A are sectionalviews taken in the direction parallel to the scanning plane, and FIGS.31B through 33B are sectional views taken in the direction perpendicularto the scanning plane.

FIGS. 34 through 36 are aberration diagrams in the direction parallel tothe scanning plane in the examples of lens arrangement according to thefourth embodiment.

FIGS. 37 through 39 are aberration diagrams in the directionperpendicular to the scanning plane in the examples of lens arrangementaccording to the fourth embodiment.

FIG. 40 is a schematic view of a laser beam printer employing the tilterror corrective scanning optical system according to the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described hereinafter by referring tospecific examples of embodiments. A tilt error corrective scanningoptical system according to the invention is used in a laser scanningapparatus such as a laser beam printer.

As shown in FIG. 40, the laser scanning apparatus comprises asemiconductor laser 1, a collimator lens 2, a cylindrical lens 3, apolygonal mirror 4, an fθ lens 5 and a photoreceptor drum 6.

The semiconductor laser 1 emits a laser beam B directly modulated inaccordance with image data. The laser beam B, which is one example of abeam, is shaped by the collimator lens 2 into parallel rays. Theparallel rays are converged into a line by the cylindrical lens 3 whichis one example of linear image forming optical element. The laser beam Bthen forms an image on a deflecting surface 4a of the polygonal mirror 4which is one example of deflecting means. The laser beam B reflected anddeflected by the deflecting surface 4a with a rotation of the polygonalmirror 4 proceeds to the fθ lens 5 which is one example of scanningimage forming optical device. The fθ lens 5 causes the laser beam B toscan the photoreceptor drum 6 in a direction indicated by reference A inthe drawing, thereby forming an image on the drum 6.

The tilt error corrective scanning optical system includes the describedlinear image forming optical element 3 and the scanning image formingoptical device 5 having two lenses G1 and G2, and eliminates pitchslippage of scanning lines resulting from tilt errors of deflectingsurfaces 4a.

As described hereinbefore, there are four basic embodiments of theinvention, and each embodiment includes two to five variations. Eachexample is illustrated by the views showing a lens arrangement, anaberration diagram for a direction parallel to a scanning plane and anaberration diagram for a direction perpendicular to the scanning plane.The relationship between the various embodiments and the drawings arelisted en bloc in Table 1 hereunder.

                  TABLE 1                                                         ______________________________________                                                                Aberrations                                                                             Aberrations                                                         Following Across                                      Embodiments                                                                             Lens Arrangements                                                                           Scan Plane                                                                              Scan Plane                                  ______________________________________                                        1-1       FIGS. 1A & 1B FIG. 6    FIG. 11                                     1-2       FIGS. 2A & 2B FIG. 7    FIG. 12                                     1-3       FIGS. 3A & 3B FIG. 8    FIG. 13                                     1-4       FIGS. 4A & 4B FIG. 9    FIG. 14                                     1-5       FIGS. 5A & 5B FIG. 10   FIG. 15                                     2-1       FIGS. 16A & 16B                                                                             FIG. 18   FIG. 20                                     2-2       FIGS. 17A & 17B                                                                             FIG. 19   FIG. 21                                     3-1       FIGS. 22A & 22B                                                                             FIG. 25   FIG. 28                                     3-2       FIGS. 23A & 23B                                                                             FIG. 26   FIG. 29                                     3-3       FIGS. 24A & 24B                                                                             FIG. 27   FIG. 30                                     4-1       FIGS. 31A & 31B                                                                             FIG. 34   FIG. 37                                     4-2       FIGS. 32A & 32B                                                                             FIG. 35   FIG. 38                                     4-3       FIGS. 33A & 33B                                                                             FIG. 36   FIG. 39                                     ______________________________________                                    

Factors for the various embodiments incorporating specific constructionsof the scanning image forming optical device 5 will be set forthhereinafter. The single asterisk (*) after the reference for thereflecting surface signifies a cylindrical surface, and the doubleasterisk (**) signifies a toric surface.

In the aberration diagrams for the direction parallel to the scanningplane, an ideal image height for realizing a uniform velocity scanningby the beam is expressed by f.θ, wherein θ is an incident angle, i.e. anangle formed between the deflected beam and a lens optical axis, and fis a focal length of all scanning optical devices in the directionparallel to the scanning plane, and distortions are expressed by thepercentage of difference between the ideal image height and actual imageheights as follows:

    {(y'-fθ)/fθ}×100 (%)

wherein y' is an actual image height.

In the factors for the various embodiments, 2ω is a maximum incidentangle, n1 is the refractive index (in 780 nm) of an optical materialforming the first lens G1, n2 is the refractive index (in 780 nm) of anoptical material forming the second lens G2, f1H is the focal length ofthe first lens G1 in the direction parallel to the scanning plane, f2His the focal length of the second lens G2 in the direction parallel tothe scanning plane, fV is the focal length of all scanning opticaldevices in the direction perpendicular to the scanning plane, f1V is thefocal length of the first lens G1 in the direction perpendicular to thescanning plane, and f2V is the focal length of the second lens G2 in thedirection perpendicular to the scanning plane. The unit of the numericalvalues for focal lengths, radii of curvature and spaces (D₀ -D₃) onoptical axis is millimeter unless otherwise indicated.

    ______________________________________                                        (Embodiment 1-1)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.5                                        r.sub.1 = -168.35                                                                        r.sub.1V = -168.35                                                 G1                      d.sub.1 = 19.5                                                                          n.sub.1 = 1.609                             r.sub.2 * = ∞                                                                      r.sub.2V = 67.20                                                                           d.sub.2 = 2.0                                         r.sub.3 = ∞                                                                        r.sub.2V = ∞                                                 G2                      d.sub.3 = 22.0                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -74.10                                                                      r.sub.4V = -21.87                                                  f.sub.1H = -276.391 f.sub.1V = -76.459 f.sub.1H /f.sub.1V                     ______________________________________                                        = 3.61                                                                    

    ______________________________________                                        (Embodiment 1-2)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 12.0                                        r.sub.1 = -128.91                                                                        r.sub.1V = -128.91                                                 G1                      d.sub.1 = 17.0                                                                          n.sub.1 = 1.511                             r.sub.2 * = ∞                                                                      r.sub.2V = 50.91                                                                           d.sub.2 = 2.0                                         r.sub.3 = ∞                                                                        r.sub.3V = ∞                                                 G2                      d.sub.3 = 23.0                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -72.47                                                                      r.sub.4V  = -21.23                                                 f.sub.1H = -252.184 f.sub.1V = -69.188 f.sub.1H /f.sub.1V                     ______________________________________                                        = 3.64                                                                    

    ______________________________________                                        (Embodiment 1-3)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 15.6                                        r.sub.1 * = ∞                                                                      r.sub.1V = -8.95                                                   G1                      d.sub.1 = 8.6                                                                           n.sub.1 = 1.511                             r.sub.2 = 506.15                                                                         r.sub.2V = 506.15                                                                          d.sub.2 = 6.4                                         r.sub.3 = -623.06                                                                        r.sub.3V  = -623.06                                                G2                      d.sub.3 = 40.4                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -80.87                                                                      r.sub.4V  = -25.21                                                 f.sub.1H = -990.177 f.sub.1V = -17.107 f.sub.1H /f.sub.1V                     ______________________________________                                        = 57.89                                                                   

    ______________________________________                                        (Embodiment 1-4)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 15.5                                        r.sub.1 * = ∞                                                                      r.sub.1V = --11.63                                                 G1                      d.sub.1 = 8.6                                                                           n.sub.1 = 1.609                             r.sub.2 = 557.18                                                                         r.sub.2V = 557.18                                                                          d.sub.2 = 6.4                                         r.sub.3 = -631.58                                                                        r.sub.3V  = -631.58                                                G2                      d.sub.3 = 40.3                                                                          n.sub.2 = 1.786                             r.sub.4 = -80.49                                                                         r.sub.4V = -25.18                                                  f.sub.1H = -914.748 f.sub.1V = -18.595 f.sub.1H /f.sub.1V                     ______________________________________                                        = 49.19                                                                   

    ______________________________________                                        (Embodiment 1-5)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.0                                        r.sub.1 = -200.62                                                                        r.sub.1V = -200.62                                                 G1                      d.sub.1 = 7.0                                                                           n.sub.1 = 1.786                             r.sub.2 * = ∞                                                                      r.sub.2V = 43.65                                                                           d.sub.2 = 1.1                                         r.sub.3 = ∞                                                                        r.sub.3V = ∞                                                 G2                      d.sub.3 = 42.0                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -73.30                                                                      r.sub.4V = -23.17                                                  f.sub.1H = -255.334 f.sub.1V = -45.063 f.sub.1H /f.sub.1V                     ______________________________________                                        = 5.67                                                                    

    ______________________________________                                        (Embodiment 2-1)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 10.0                                        r.sub.1 *= -∞                                                                      r.sub.1V = -55.08                                                  G1                      d.sub.1 = 5.0                                                                           n.sub.1 = 1.511                             r.sub.2 = ∞                                                                        r.sub.2V = 26.25                                                                           d.sub.2 = 1.2                                         r.sub.3 = -241.40                                                                        r.sub.3V = -241.40                                                 G2                      d.sub.3 = 51.3                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -76.34                                                                      r.sub.4V = -24.20                                                  ______________________________________                                    

    ______________________________________                                        (Embodiment 2-2)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 11.0                                        r.sub.1 = ∞                                                                        r.sub.1V = ∞                                                 G1                      d.sub.1 = 5.0                                                                           n.sub.1 = 1.511                             r.sub.2 * = ∞                                                                      r.sub.2V = 25.48                                                                           d.sub.2 = 1.2                                         r.sub.3 = -229.63                                                                        r.sub.3V = -229.63                                                 G2                      d.sub.3 = 51.6                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -75.59                                                                      r.sub.4V = -24.78                                                  ______________________________________                                    

    ______________________________________                                        (Embodiment 3-1)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 12.5                                        r.sub.1 * = -165.22                                                                      r.sub.1V = ∞                                                 G1                      d.sub.1 = 19.8                                                                          n.sub.1 = 1.609                             r.sub.2 * = ∞                                                                      r.sub.2V = 60.98                                                                           d.sub.2 = 2.2                                         r.sub.3 = ∞                                                                        r.sub.3V = ∞                                                 G2                      d.sub.3 = 22.5                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -73.95                                                                      r.sub.4V = -21.89                                                  f.sub.1H = -271.251 f.sub.1V = -100.117 f.sub.1H /f.sub.1V                    ______________________________________                                        = 2.71                                                                    

    ______________________________________                                        (Embodiment 3-2)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 15.5                                        r.sub.1 * = ∞                                                                      r.sub.1V = -7.92                                                   G1                      d.sub.1 = 8.5                                                                           n.sub.1 = 1.511                             r.sub.2 * = 509.21                                                                       r.sub.2V = ∞                                                                         d.sub.2 = 6.4                                         r.sub.3 = -626.78                                                                        r.sub.3V = -626.78                                                 G2                      d.sub.3 = 40.4                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -80.94                                                                      r.sub.4V = -25.02                                                  f.sub.1H = -996.16 f.sub.1V = -15.484 f.sub.1H /f.sub.1V                      ______________________________________                                        = 64.33                                                                   

    ______________________________________                                        (Embodiment 3-3)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.0                                        r.sub.1 * = -200.97                                                                      r.sub.1V = ∞                                                 G1                      d.sub.1 = 10.0                                                                          n.sub.1 = 1.786                             r.sub.2 = ∞                                                                        r.sub.2V = +49.10                                                                          d.sub.2 = 1.1                                         r.sub.3 = ∞                                                                        r.sub.3V = ∞                                                 G2                      d.sub.3 = 39.0                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -73.33                                                                      r.sub.4V = -23.21                                                  f.sub.1H = -255.787 f.sub.1V = -62.490 f.sub.1H /f.sub.1V                     ______________________________________                                        = 4.09                                                                    

    ______________________________________                                        (Embodiment 4-1)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.5                                        r.sub.1 * = -186.29                                                                      r.sub.1V = ∞                                                 G1                      d.sub.1 = 22.0                                                                          n.sub.1 = 1.609                             r.sub.2 = 2701.95                                                                        r.sub.2V = 2701.95                                                                         d.sub.2 = 2.0                                         r.sub.3 * = ∞                                                                      r.sub.3V = -128.20                                                 G2                      d.sub.3 = 23.0                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -74.91                                                                      r.sub.4V = -23.28                                                  f.sub.1H = -285.296                                                           ______________________________________                                    

    ______________________________________                                        (Embodiment 4-2)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.5                                        r.sub.1 * = ∞                                                                      r.sub.1V = ∞                                                 G1                      d.sub.1 = 18.0                                                                          n.sub.1 = 1.609                             r.sub.2 = 364.35                                                                         r.sub.2V = ∞                                                                         d.sub.2 = 10.0                                        r.sub.3 * = ∞                                                                      r.sub.3V = -99.18                                                  G2                      d.sub.3 = 22.8                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -84.33                                                                      r.sub.4V = -24.31                                                  f.sub.1H = -598.170                                                           ______________________________________                                    

    ______________________________________                                        (Embodiment 4-3)                                                              f = 125, F No. = 50, 2ω = 97°                                    Radii of   Radii of                                                           Curvature  Curvature                                                          (Main Scan (Aux. Scan   On-Axis   Refractive                                  Direction) Direction)   Distance  Indices                                     ______________________________________                                        [Deflection                                                                   Point]                                                                                                d.sub.0 = 13.5                                        r.sub.1 * = -386.87                                                                      r.sub.1V = ∞                                                 G1                      d.sub.1 = 16.4                                                                          n.sub.1 = 1.609                             r.sub.2 * = 659.36                                                                       r.sub.2V = ∞                                                                         d.sub.2 = 6.0                                         r.sub.3 = ∞                                                                        r.sub.3V = -93.06                                                  G2                      d.sub.3 = 24.7                                                                          n.sub.2 = 1.786                             r.sub.4 ** = -79.66                                                                      r.sub.4V = -23.15                                                  f.sub.1H = -397.923                                                           ______________________________________                                    

What is claimed is:
 1. A tilt error corrective scanning optical systemfor a system having deflecting means for deflecting and reflecting abeam of light, comprising:a linear image forming optical device forcausing a beam emitted from a light source to form a linear image on adeflecting and reflecting surface of said deflecting means, and ascanning image forming optical device for causing the beam reflected anddeflected by said deflecting means to form an image on a scanned object,said scanning image forming optical device consisting of a first lensdisposed between said deflecting means and said scanned object, and asecond lens disposed at a side of said first lens opposed to saidscanned object, wherein said first lens includes a cylindrical surface,and said second lens includes a toric surface.
 2. A tilt errorcorrective scanning optical system as claimed in claim 1, wherein saidfirst lens has a negative refracting power in a direction perpendicularto a scanning plane.
 3. A tilt error corrective scanning optical systemas claimed in claim 2, wherein said cylindrical surface of said firstlens is defined on a surface of said first lens opposed to saiddeflecting means.
 4. A tilt error corrective scanning optical system asclaimed in claim 3, wherein said second lens defines a concave surfaceopposed to said deflecting means.
 5. A tilt error corrective scanningoptical system as claimed in claim 2, wherein said cylindrical surfaceof said first lens is defined on a surface of said first lens opposed tosaid scanned object.
 6. A tilt error corrective scanning optical systemas claimed in any one of claims 2 through 5, wherein said first lens perse as a whole has a negative refracting power in a direction parallel tothe scanning plane.
 7. A tilt error corrective scanning optical systemas claimed in claim 6, wherein said first lens satisfies the followingcondition:

    |f1H/f1V|>2

wherein f1H is a focal length of said first lens in the directionparallel to the scanning plane, and f1V is a focal length of said firstlens in the direction perpendicular to the scanning plane.
 8. A tilterror corrective scanning optical system as claimed in claim 1, whereinsaid scanning image forming optical device is so arranged that thedeflecting and reflecting surface and said scanned object are set in anoptical conjugate relationship.
 9. A tilt error corrective scanningoptical system for a system having deflecting means for deflecting andreflecting a beam of light, comprising:a linear image forming opticaldevice for causing a beam emitted from a light source to form a linearimage on a deflecting and reflecting surface of said deflecting means,and a scanning image forming optical device for causing the beamreflected and deflected by said deflecting means to form an image on ascanned object, said scanning image forming optical device consisting ofa first lens disposed between said deflecting means and said scannedobject, and a second lens disposed at a side of said first lens opposedto said scanned object, wherein said first lens comprises a cylindricallens having no refracting power in a direction parallel to a scanningplane, and said second lens includes a toric surface.
 10. A tilt errorcorrective scanning optical system as claimed in claim 9, wherein saidfirst lens has a negative refracting power in a direction perpendicularto the scanning plane.
 11. A tilt error corrective scanning opticalsystem as claimed in claim 10, wherein said first lens includes acylindrical surface on a surface of said first lens opposed to saiddeflecting means to have a negative refracting power in the directionperpendicular to the scanning plane.
 12. A tilt error correctivescanning optical system as claimed in claim 11, wherein said second lensincludes a surface opposed to said deflecting means and having anegative refracting power.
 13. A tilt error corrective scanning opticalsystem as claimed in claim 9, wherein said scanning image formingoptical device is so arranged that the deflecting and reflecting surfaceand said scanned object are set in an optical conjugate relationship.14. A tilt error corrective scanning optical system for a system havingdeflecting means for deflecting and reflecting a beam of light,comprising:a linear image forming optical device for causing a beamemitted from a light source to form a linear image on a deflecting andreflecting surface of said deflecting means, and a scanning imageforming optical device for causing the beam reflected and deflected bysaid deflecting means to form an image on a scanned object, saidscanning image forming optical device consisting of a first lensdisposed between said deflecting means and said scanned object, and asecond lens disposed at a side of said first lens opposed to saidscanned object, wherein said first lens includes a first cylindricalsurface having an axis extending perpendicular to a scanning plane and asecond cylindrical surface having an axis extending parallel to thescanning plane, and said second lens includes a toric surface.
 15. Atilt error corrective scanning optical system as claimed in claim 14,wherein said first lens has a negative refracting power in a directionperpendicular to the scanning plane.
 16. A tilt error correctivescanning optical system as claimed in claim 15, wherein said secondcylindrical surface is defined on a surface of said first lens opposedto said deflecting means to have a negative refracting power.
 17. A tilterror corrective scanning optical system as claimed in claim 15, whereinsaid second cylindrical surface is defined on a surface of said firstlens opposed to said scanned object to have a negative refracting power.18. A tilt error corrective scanning optical system as claimed in claim17, wherein said first lens has a negative refracting power in adirection parallel to the scanning plane.
 19. A tilt error correctivescanning optical system as claimed in any one of claims 15 through 18,wherein said first lens satisfies the following condition:

    |f1H/f1V|>2

wherein f1H is a focal length of said first lens in the directionparallel to the scanning plane, f1V is a focal length of said first lensin the direction perpendicular to the scanning plane.
 20. A tilt errorscanning optical system as claimed in claim 16, wherein said first lenshas a negative refracting power in a direction parallel to the scanningplane.
 21. A tilt error scanning optical system as claimed in claim 12,wherein said first lens has a negative refracting power in a directionparallel to the scanning plane.
 22. A tilt error corrective scanningoptical system as claimed in claim 14, wherein said scanning imageforming optical device is so arranged that the deflecting and reflectingsurface and said scanned object are set in an optical conjugaterelationship.
 23. A tilt error corrective scanning optical system for asystem having deflecting means for deflecting and reflecting a beam oflight, comprising:a linear image forming optical device for causing abeam emitted from a light source to form a linear image on a deflectingand reflecting surface of said deflecting means, and a scanning imageforming optical device for causing the beam reflected and deflected bysaid deflecting means to form an image on a scanned object, saidscanning image forming optical device consisting of a first lensdisposed between said deflecting means and said scanned object, and asecond lens disposed at a side of said first lens opposed to saidscanned object, wherein said first lens includes a cylindrical surfacehaving an axis extending perpendicular to a scanning plane and a secondlens includes a cylindrical surface having an axis extending parallel tothe scanning plane, and a toric surface.
 24. A tilt error correctivescanning optical system as claimed in claim 23, said cylindrical surfaceof said second lens is defined on a surface of said second lens opposedto said deflecting means to have a negative refracting power in adirection perpendicular to the scanning plane.
 25. A tilt errorcorrective scanning optical system as claimed in claim 24, wherein saidfirst lens has a negative refracting power in a direction parallel tothe scanning plane.
 26. A tilt error corrective scanning optical systemas claimed in claim 23, wherein said scanning image forming opticaldevice is so arranged that the deflecting and reflecting surface andsaid scanned object are set in an optical conjugate relationship.
 27. Atilt error corrective scanning optical system for a system havingdeflecting means for deflecting and reflecting a beam of light,comprising:a linear image forming optical device for causing a beamemitted from a light source to form a linear image in a deflecting andreflecting surface of said deflecting means, and a scanning imageforming optical device for causing the beam reflected and deflected bysaid deflecting means to form an image on a scanned object, saidscanning image forming optical device consisting of a first lensdisposed between said deflecting means and said scanned object, and asecond lens disposed at a side of said first lens opposed to saidscanned object, wherein said first lens includes a toric surface opposedto said scanned object, and any one of the remaining surfaces, that isto say, a surface of said second lens opposed to said deflecting means,a surface of said first lens opposed to said scanned object and asurface of said first lens opposed to said deflecting means furtherdefines a cylindrical surface having a refracting power in a directionperpendicular to a scanning plane.
 28. A tilt error corrective scanningoptical system as claimed in claim 21, wherein said scanning imageforming optical device is so arranged that the deflecting and reflectingsurface and said scanned object are set in an optical conjugaterelationship.
 29. A tilt error corrective laser beam printercomprising:a laser beam source for emitting a laser beam modulated inaccordance with image data, a collimator lens for shaping the laser beaminto parallel rays, a linear image forming optical device for convergingthe laser beam in parallel rays into a line, deflecting means forreflecting and deflecting the laser beam converged into a line toward ascanned object, and a scanning image forming optical device for causingthe laser beam reflected and deflected by a deflecting and reflectingsurface of said deflecting means to form an image on said scannedobject, said scanning image forming optical device consisting of a firstlens disposed between said deflecting means and said scanned object, anda second lens disposed at a side of said first lens opposed to saidscanned object, wherein said first lens includes a cylindrical surface,and said second lens includes a toric surface.
 30. A laser beam printeras claimed in claim 29 wherein said linear image forming optical devicecomprises a cylindrical lens.
 31. A tilt error corrective scanningoptical system as claimed in claim 29, wherein said scanning imageforming optical device is so arranged that the deflecting and reflectingsurface and said scanned object are set in an optical conjugaterelationship. .Iadd.
 32. A scanning optical system for use in a laserprinter comprising:a semiconductor laser; a collimator lens receivinglaser light from said semiconductor laser and emitting substantiallyparallel light rays; a cylindrical lens having a curvature in a crosssection taken in a first direction normal to a main scan direction, saidcylindrical lens receiving said parallel light rays emitted by saidcollimator lens and images said laser light at a focusing point in saidcross section taken in said first direction; a deflector which deflectslight rays transmitted by said cylindrical lens, said deflector beingdisposed on a downstream side of said cylindrical lens with respect tosaid light rays; and an anamorphic scanning lens unit which convergeslight rays deflected by said deflector at a point on a scanning surface;wherein said anamorphic scanning lens unit has a two-element compositioncomprising, in order from a side nearest said deflector; a first lenshaving a negative lens element with a concave spherical surface on aside facing said deflector and a concave cylindrical surface on a sidefacing said scanning surface, said concave cylindrical surface having acurvature in said cross section taken in said first direction, and asecond lens having a planar surface on a side facing said deflector anda convex toric surface on a side facing said scanning surface, saidconvex toric surface having a stronger curvature in said cross sectiontaken in said first direction. .Iaddend. .Iadd.
 33. A scanning opticalsystem for use in a laser printer as claimed in claim 32, wherein saiddeflector is a polygonal mirror. .Iaddend. .Iadd.
 34. A scanning opticalsystem for use in a laser printer comprising:a semiconductor laser;first means for focusing the light from said laser onto a focusing pointin a first dimension while leaving the light unfocused in a seconddimension normal to said first dimension; a deflector which deflectslight rays transmitted by said first means, said deflector beingdisposed on a downstream side of said first means with respect to lightrays; and an anamorphic scanning lens unit which converges light raysdeflected by said deflector at a point on a scanning surface; whereinsaid anamorphic scanning lens unit has a two-element compositioncomprising, in order from a side nearest said deflector; a first lenshaving a negative lens element with a concave spherical surface on aside facing said deflector and a concave cylindrical surface on a sidefacing said scanning surface, said concave cylindrical surface having acurvature in a cross section taken in a direction normal to said firstdimension, and a second lens having a planar surface on a side facingsaid deflector and a convex toric surface on a side facing said scanningsurface, said convex toric surface having a stronger curvature in saidcross section taken in said direction normal to said first dimension..Iaddend. .Iadd.35. A tilt error corrective scanning optical systemhaving a deflecting means for deflecting and reflecting a beam of light,comprising: a linear image forming optical device for causing the beamemitted from a light source to form a linear image in a direction andreflecting surface of said deflecting means, said linear image beingparallel to a direction normal to a first dimension and an anamorphicscanning lens unit which converges the beam deflected by said deflectingmeans at a point on a scanning surface; wherein said anamorphic scanninglens unit has a two-element composition comprising, in order from a sidenearest said deflecting means; a first lens having a negative lenselement with a concave spherical surface on a side facing saiddeflecting means and a concave cylindrical surface on a side facing saidscanning surface, said concave cylindrical surface having a curvature ina cross section taken in a direction normal to said first dimension, anda second lens having a planar surface on a side facing said deflectingmeans and a convex toric surface on a side facing said scanning surface,said convex toric surface having a stronger curvature in said crosssection taken in said direction normal to said first dimension..Iaddend.